What is the directrix 2x^2-19x+9 ?

The directrix 2x^2-19x+9 is y=-145/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix 2x^2-19x+9

directrix

2 x^{2} - 19 x + 9

y = - \frac{145}{4}

Solution steps

Rewrite

y = 2 x^{2} - 19 x + 9

in the standard form

4 \cdot \frac{1}{8} (y - (- \frac{289}{8})) = (x - \frac{19}{4})^{2}

(h, k) = (\frac{19}{4}, - \frac{289}{8}), p = \frac{1}{8}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(\frac{19}{4}, - \frac{289}{8})

y-coordinate

y = - \frac{289}{8} - p

y = - \frac{289}{8} - \frac{1}{8}

Refine

y = - \frac{145}{4}

(x + 3)^{2} = - y

x^{2} + 4

x^{2} - 4 x + 5

y = \frac{1}{2} x^{2} + 9 x + 8

x = \frac{1}{4} y^{2}